You can use coins for purchasing new puzzle packs from the Puzzle shop. The price in coins is indicated on every paid pack.
If you open the preview of any pack, you will see Get it button in the right upper corner. Press the button and then choose the coins option.
You can earn coins by solving puzzles and watching bonus videos.
If you need more coins, you can purchase them in Coins bank - click on the plus sign next to the amount of coins: